A new hybrid dynamic mode decomposition (HDMD) algorithm is proposed to estimate the azimuth and elevation angles of multiple independent sources for two-dimensional (2D) massive MIMO systems with the uniform rectangular array (URA). To this end, the proposed hybrid scheme integrates the modified DMD with the augmented DMD. By treating the received data as spatial-spatial correlated signals, the modified DMD is first used to decompose these signals into spatial DMD spectrum and corresponding spatial dynamic modes. The obtained spatial DMD spectrum directly yields the electrical angle in the y-direction. Then, the corresponding electrical angle in the x-direction is computed using augmented DMD on the spatial dynamic modes. Finally, the azimuth and elevation angles are extracted through the inversion relationship within the URA. This correlated decomposition method automatically matches estimated azimuth and elevation angles. Moreover, the spatial DMD spectrum can determine the number of signal sources, enabling the method to be used without prior knowledge of the source number. Some numerical examples are performed to demonstrate the effectiveness and robustness of the proposed method. It is found that compared with other similar methods, the proposed method has better performance in 2D angles estimation. Therefore, our work provides an efficient source localization technique for massive MIMO systems.


Electrical and Computer Engineering


Asian Office of Aerospace Research and Development, Grant 104005008

Keywords and Phrases

automatic pairing; Azimuth and elevation estimation; data-driven approach; hybrid dynamic mode decomposition; unknown source number

International Standard Serial Number (ISSN)

1939-9359; 0018-9545

Document Type

Article - Journal

Document Version


File Type





© 2024 Institute of Electrical and Electronics Engineers, All rights reserved.

Publication Date

01 Feb 2023